A190116 a(n) = n*n', where n' is the arithmetic derivative (A003415) of n.

0, 2, 3, 16, 5, 30, 7, 96, 54, 70, 11, 192, 13, 126, 120, 512, 17, 378, 19, 480, 210, 286, 23, 1056, 250, 390, 729, 896, 29, 930, 31, 2560, 462, 646, 420, 2160, 37, 798, 624, 2720, 41, 1722, 43, 2112, 1755, 1150, 47, 5376, 686, 2250

Offset: 1

Author

Giorgio Balzarotti, May 04 2011

Keywords

• nonn

Comments

Sequence is not injective. 4153248 is the smallest number that occurs more than once, as a(1368) and as a(2277). See example in A327861. - Antti Karttunen, Sep 29 2019

Examples

			For n=4, 4'= 4, 4*4' = 16, so a(4)=16.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A327861 (number of times n occurs in this sequence).

Programs

Maple

der:=n->n*add(op(2,p)/op(1,p),p=ifactors(n)[2]):
seq(der(n)*n,n=1..50);

Mathematica

A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]]; Table[n*A003415[n], {n, 1, 50}] (* G. C. Greubel, Dec 29 2017 *)

PARI

a(n) = n*sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]); \\ Michel Marcus, Dec 30 2017

Formula

a(n) = A085731(n) * A086130(n). - Michel Marcus, Oct 24 2013